If \[{{C}_{r}}\] stands for \[^{n}{{C}_{r}}\], the sum of the given series\[\frac{2(n/2)!(n/2)!}{n!}[C_{0}^{2}-2C_{1}^{2}+3C_{2}^{2}-.....+{{(-1)}^{n}}(n+1)C_{n}^{2}]\], Where n is an even positive integer, is [IIT 1986]

If \[{{C}_{r}}\] stands for \[^{n}{{C}_{r}}\], the sum of the given se

1.	If \[{{C}_{r}}\] stands for \[^{n}{{C}_{r}}\], the sum of the given series\[\frac{2(n/2)!(n/2)!}{n!}[C_{0}^{2}-2C_{1}^{2}+3C_{2}^{2}-.....+{{(-1)}^{n}}(n+1)C_{n}^{2}]\], Where n is an even positive integer, is [IIT 1986]
A.	0
B.	\[{{(-1)}^{n/2}}(n+1)\]
C.	\[{{(-1)}^{n}}(n+2)\]
D.	\[{{(-1)}^{n/2}}(n+2)\]
Answer» E.

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If \[{{C}_{r}}\] stands for \[^{n}{{C}_{r}}\], the sum of the given series\[\frac{2(n/2)!(n/2)!}{n!}[C_{0}^{2}-2C_{1}^{2}+3C_{2}^{2}-.....+{{(-1)}^{n}}(n+1)C_{n}^{2}]\], Where n is an even positive integer, is [IIT 1986]

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